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Prime tight frames

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Abstract

We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames and use thischaracterization to suggest effective analysis and synthesis computation strategies for such frames. Finally, we describe all prime frames constructed from the spectral tetris method, and, as a byproduct, we obtain a characterization of when the spectral tetris construction works for redundancies below two.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet 303, 2800, Kgs. Lyngby, Denmark

    Jakob Lemvig

  2. Department of Mathematics, University of Maryland, 8803 Pisgah Drive, Clinton, MD, 20735, USA

    Christopher Miller

  3. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Kasso A. Okoudjou

Authors
  1. Jakob Lemvig
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  2. Christopher Miller
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  3. Kasso A. Okoudjou
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Correspondence to Jakob Lemvig.

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Communicated by: Yang Wang

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Lemvig, J., Miller, C. & Okoudjou, K.A. Prime tight frames. Adv Comput Math 40, 315–334 (2014). https://doi.org/10.1007/s10444-013-9309-0

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  • DOI: https://doi.org/10.1007/s10444-013-9309-0

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